摘要
针对下层为线性规划的非线性双层规划问题,提出了一种基于下层对偶理论的遗传算法。首先利用下层对偶问题可行域的极点对上层变量的取值域进行划分,使得每一个划分区域对应一个极点。根据原-对偶问题最优解的关系,确定每个划分区域对应的下层最优解。其次利用罚函数方法处理了上层约束,设计了一个依赖于种群变化的动态罚因子。对20个测试问题的数值结果表明,所提出的算法是可行有效的。
For nonlinear bilevel programming problems in which the follower＇ s programming is linear in both xandy, a genetic algorithm based on the duality theory of the follower＇s problem is proposed. First, the definition domain of leader＇ s variables is divided into several sub-regions according to the extreme points of the feasible region of the follower＇s dual problem such that each divided sub-region corresponds to an extreme point. As a result, the follower＇ s optimal solutions corresponding to each divided sub-region can be gotten by using the relation between the prime-dual optimal solutions. Then, an adaptive parameter is given when the penalty method is used to deal with the leader＇ s constraints. The numerical results on 20 test problems illustrate that the proposed algorithm is feasible and efficient.
出处
《运筹与管理》
CSCD
2008年第6期6-10,共5页
Operations Research and Management Science
关键词
非线性双层规划
遗传算法
对偶理论
极点
最优解
nonlinear bilevel programming
genetic algorithm
duality theory
extreme points
optimal solutions
